Inverse analysis is a promising method for addressing a common problem in stream ecology: how to estimate material and energy flows through food webs when the total number of flows greatly exceeds the number of measured flows. Inverse analyses provide solutions to systems of linear difference equations, where each equation corresponds to a flow between 2 foodweb compartments. Physiological and isotopic constraints are used to reduce the number of possible solutions and to ensure that flow magnitudes are realistic. We used inverse methods to develop models of C and N flows through the food web in Kaiwiki Stream, a forested stream on the island of Hawaii. The empirical data used in the models included measurements of respiration and detritus ingestion and particulate organic matter dynamics. Constraints for the models included stable isotope ratios and assimilation and production efficiencies. Sensitivity analyses indicated that the models were robust to changes in the values of most empirical measurements. The models elucidated community- and ecosystem-level properties of Kaiwiki Stream that would have been obscured in simpler tracer or budget models. Among those properties are the flows of dissolved organic C and N through the food web, the roles of bacteria, fungi, and fruit in metazoan diets, and the differences in primary dietary sources of C and N, indicating differential assimilation of ingested food. The modeled C and N flow networks for Kaiwiki Stream had dissimilar structures, which might reflect a combination of differential C and N assimilation and dissimilar effects of physical processes on C and N flows between nonliving pools. Rates of ecosystem processes estimated by inverse analysis (e.g., gross primary productivity, community respiration) were comparable with rates measured in other tropical and temperate forested streams. Our study demonstrates the utility of inverse methods for reconstructing food webs, estimating material and energy flow rates, and generating hypotheses.
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